ABCD

Propagation of a gaussian beam through free space and an arbitrary configuration thin lenses using the ABCD formalism¹.

Maxwell's equations give us the equation of motion for a propagatin gelectric field:

Under the assumption that and we arrive at the Helmholtz equation

From which, we find the field:

where

is the Rayleigh range,

is the Gouy phase,

is the radius of curvature of the wavefront, and

is the radius of the beam.

We define the 'complex-q' parameter as

When the beam propagates through free space or a thin lens, it transforms according to

where

for propagation by a distance and

for transmission through a thin lens with focal length

The thick lens implementation is taken from²

Requirements

• numpy
• matplotlib

References

Footnotes

1. P. W. Milonni and J. H. Eberly, Lasers (John Wiley and Sons, New York, 1988). ↩

2. S. Nemoto, Applied Optics, 29(6), 809 (1990). ↩